17. Consider the nuclear activity. Which one of the following elements is the most unstable one?
(A) He²
(B) Na¹¹
(C) Xe⁵⁴
(D) Pb⁸²
(E) Ra⁸⁸

18. Which one of the following description of the matter wave Ψ(x, t) is correct? (A) The probability of finding a particle at position x and time t is proportional to the value of |Ψ(x, t)|². (B) The probability of finding a particle at position x and time t is proportional to the value of |Ψ(x, t)|. (C) The probability of finding a particle at position x and time t is proportional to the value of Ψ(x, t). (D) The mass distribution of a particle at position x and time t is proportional to the value of |Ψ(x, t)|². (E) The mass distribution of a particle at position x and time t is proportional to the value of |Ψ(x, t)|.

19. According to the Bohr model of hydrogen atom, the wave function of the electron forms a standing wave inside the atom. This result is derived from what postulate? (A) quantization of energy of the electron (B) quantization of velocity of the electron (C) quantization of momentum of the electron (D) quantization of angular momentum of the electron (E) quantization of charge of the electron

20. Which one of the following statement of superconductor is wrong? (A) The resistivity goes to zero. (B) When temperature increases higher than its critical temperature, the superconductivity will disappear. (C) The electric field inside a superconductor must be zero. (D) The magnetic field inside a superconductor must be zero. (E) The conductivity goes to infinity.

21. A solid rod is hanged by a wire attached to its right, as shown in the figure. The left of the rod contacts the wall with friction force. If the coefficient of static friction is μs, what is the maximum value of θ that the rod can keep stable? (A) θ = tan⁻¹ μs (B) θ = cot⁻¹ μs (C) θ = sin⁻¹ μs (D) θ = cos⁻¹ μs (E) θ = sec⁻¹ μs

22. As shown in the figure, a copper strip of width d = 2 (cm), carrying a current I = 100 (mA), is put in an external magnetic field B = 0.02 (tesla). A potential difference ΔV = VL - VR is measured to be 5 (mV). What is the drift velocity of the charge carrier? (A) 12.5 (m/sec) (B) 20 (m/sec) (C) 25 (m/sec) (D) 40 (m/sec) (E) 50 (m/sec)

23. 2-kg ice at -10°C is added to 5-kg water at 45°C. What is the final temperature of the system? The specific heat of ice and water are 2100 J/kg-K and 4190 J/kg-K, respectively. The latent heat of ice-water transition is 334000 J/kg. (A) 7.5 °C (B) 7.7 °C (C) 7.9 °C (D) 8.1 °C (E) 8.3 °C

24. Find the lower limit of γ-ray frequency for pair production (electron-positron creation). Note: electron and positron mass mₑ = 9.1 × 10⁻³¹ kg           speed of light c = 3 × 10⁸ m/sec           Planck's constant h = 6.6 × 10⁻³⁴ J-sec (A) 2.0 × 10²⁰ Hz (B) 2.5 × 10²⁰ Hz (C) 3.0 × 10²⁰ Hz (D) 3.5 × 10²⁰ Hz (E) 4.0 × 10²⁰ Hz

25. Consider a quantum harmonic oscillator with mass m = 10⁻³¹ kg and resonance frequency f = 10²⁰ Hz. The ground state wave function is written as Ψ₀(x) = (4πmf/h)^(1/4) exp[-(2π²mf/h)x²]  Find the expectation value of the position ＜x＞.(A) 2.4 nm (B) 1.8 nm (C) 1.2 nm (D) 0.6 nm (E) 0 nm

1. Which of the following sugars structure below give meso-product when treated with excess sodium borohydride (NaBH4)(A) I, II(B) I(C) I, III(D) II, IV(E) IV

2. Which of the following structure is NOT a structural isomer of cyclohexanol(A) I, II(B) II, III(C) III, V(D) I, IV(E) None of the above

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